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Simplifying 100x2 + 0.01x + -5066104.5 = 0 Reorder the terms: -5066104.5 + 0.01x + 100x2 = 0 Solving -5066104.5 + 0.01x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -50661.045 + 0.0001x + x2 = 0 Move the constant term to the right: Add '50661.045' to each side of the equation. -50661.045 + 0.0001x + 50661.045 + x2 = 0 + 50661.045 Reorder the terms: -50661.045 + 50661.045 + 0.0001x + x2 = 0 + 50661.045 Combine like terms: -50661.045 + 50661.045 = 0.000 0.000 + 0.0001x + x2 = 0 + 50661.045 0.0001x + x2 = 0 + 50661.045 Combine like terms: 0 + 50661.045 = 50661.045 0.0001x + x2 = 50661.045 The x term is 0.0001x. Take half its coefficient (0.00005). Square it (0.0000000025) and add it to both sides. Add '0.0000000025' to each side of the equation. 0.0001x + 0.0000000025 + x2 = 50661.045 + 0.0000000025 Reorder the terms: 0.0000000025 + 0.0001x + x2 = 50661.045 + 0.0000000025 Combine like terms: 50661.045 + 0.0000000025 = 50661.0450000025 0.0000000025 + 0.0001x + x2 = 50661.0450000025 Factor a perfect square on the left side: (x + 0.00005)(x + 0.00005) = 50661.0450000025 Calculate the square root of the right side: 225.080085747 Break this problem into two subproblems by setting (x + 0.00005) equal to 225.080085747 and -225.080085747.Subproblem 1
x + 0.00005 = 225.080085747 Simplifying x + 0.00005 = 225.080085747 Reorder the terms: 0.00005 + x = 225.080085747 Solving 0.00005 + x = 225.080085747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00005' to each side of the equation. 0.00005 + -0.00005 + x = 225.080085747 + -0.00005 Combine like terms: 0.00005 + -0.00005 = 0.00000 0.00000 + x = 225.080085747 + -0.00005 x = 225.080085747 + -0.00005 Combine like terms: 225.080085747 + -0.00005 = 225.080035747 x = 225.080035747 Simplifying x = 225.080035747Subproblem 2
x + 0.00005 = -225.080085747 Simplifying x + 0.00005 = -225.080085747 Reorder the terms: 0.00005 + x = -225.080085747 Solving 0.00005 + x = -225.080085747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00005' to each side of the equation. 0.00005 + -0.00005 + x = -225.080085747 + -0.00005 Combine like terms: 0.00005 + -0.00005 = 0.00000 0.00000 + x = -225.080085747 + -0.00005 x = -225.080085747 + -0.00005 Combine like terms: -225.080085747 + -0.00005 = -225.080135747 x = -225.080135747 Simplifying x = -225.080135747Solution
The solution to the problem is based on the solutions from the subproblems. x = {225.080035747, -225.080135747}
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